Section: New Results
Hyperbolic Problems, Conservation laws and Gas Dynamics
The convergence analysis of numerical schemes for conservation laws with unstructured meshes with an original proof based on probabilistic argument is a striking result due to F. Lagoutière with F. Delarue,  . More generally, we refer to  for an overview of F. Lagoutière's works.
The analysis of the stability of compressible vortex sheets has been carried out in  by J.-F. Coulombel. J.-F. Coulombel also studies the stability of finite difference approximation of hyperbolic problems with boundary conditions  . He generalizes and simplifies previous results by Gustaffson-Kreiss-Sundström. The analysis is a necessary starting point for extensions to multidimensional situations. J.-F. Coulombel has obtained a detailed description of the so-called hyperbolic region for hyperbolic boundary value problems  . This gives preliminary information in order to describe the propagation of high frequency signals and their reflection on the boundary. A synthetic survey of these results can be found on  .